On the Well-Posedness and Stability Analysis of Nonlinear Fractional Integrodifferential Equations Subject to Integral Boundary Constraints

This article investigates the existence, uniqueness, and stability of solutions for a class of nonlinear fractional integrodifferential equations (NLFIDEs) with nonlocal boundary conditions in Banach algebras. By employing advanced analytical techniques within the Banach algebra framework, we rigorously establish existence and uniqueness results and analyze the stability of solutions through Ulam–Hyers and generalized stability concepts. The study considers a general class of multiterm Caputo fractional derivatives with nonlinearities depending on both the solution and its fractional derivatives, under nonlocal integral boundary conditions—a combination not previously addressed in the literature. The theoretical findings provide a solid foundation for fractional-order systems exhibiting memory and nonlocal effects, offering insights that can guide the modeling of complex phenomena. While the work is primarily theoretical, it lays the groundwork for future studies on applications of such equations in engineering and scientific problems.MSC2020 Classification: 26A33, 34A08, 34B18, 34K06, 37N40